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BOARD OF EDUCATION— THE CITY OF NEW YORK 
BUREAU OF REFERENCE. RESEARCH AND STATISTICS 



Grade Standards 

for the 

New York 
Penmanship Scale 



1920 

Publication No. 18 



r 






Grade Standards 

for the 

New York Penmanship Scale 



Issued by the Bureau of Reference, Research and Statistics 
Eugene A. Nifenecker, Director 



Anning S. Prall, 
President, Board of Education 



William L. Ettinger, 
Superintendent of Schools 



1920 

PubHcation No. 18 






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TABLE OF CONTENTS 



LIST OF TABLES. 



LIST OF FIGURES.. 
INTRODUCTION 



I. THE NEW YORK PENMANSHIP SCALE. 

1. Characteristics of the Scale _ 

2. Construction of the Scale 



PAGE 
.. 3 



II. 



MEASURING PRESENT ACHIEVEMENTS IN PENMANSHIP 14 

1. Conduct of tests __. 14 

2. General results : 14 

3. Rate of writing 18 

4. Quality of writing , 23 

(a) Form _ 23 

(b) Movement _ 27 

(c) Spacing. 29 

5. Relation of speed and quality 30 

6. Relative emphasis on quality and speed in different schools.. 39 

TENTATIVE GRADE STANDARDS IN FORM, MOVEMENT, 

SPACING AND SPEED 45 

1. The degree of penmanship ability found in the business 

world 45 

2. Tentative standards for each grade 47 

3. The value of grade standards 49 

APPENDIX A — Methods of scoring employed in survey 52 

APPENDIX B— Reliability of scoring 57 



III. 



LIBflARY OF CONGRESS 

RECEIVED 

JUL151922 

OOCUMfcNTS DlViSION 



LIST OF TABLES 



PAGE 
I. City wide median scores by grades for form, movement, spacing 

and rate — - 15 

II. Distribution of individual scores for rate of writing.,... 18 

III. Grade median rates, upper and lower quartiles 19 

IV. Grade medians, upper and lower quartiles in form 24 

V. Comparison of quartiles with medians to show overlapping 26 

VI. Grade medians, upper and lower quartiles in movement. 27 

VII. Grade medians, upper and lower quartiles in spacing. 29 

VIII. Average rate in each grade for each step on scale in form 32 

IX. Average rate in each grade for each step on scale in movement 35 

X. Average rate in each grade for each step on scale in spacing 37 

XI. Coefficients of correlations between the several elements 39 

XII. Median scores of groups of clerical employees in department stores.... 45 

XIII. Tentative standards in penmanship for the New York City Pen- 

manship Scale .,_ 47 

XIV. Average deviation per specimen from ' ' expert' ' scores for 86 prospec- 

tive judges — ^practice samples. ?. 53 

XV. Average deviation per specimen from "expert" scores for 86 pros- 
pective judges— practice samples— second tabulation... 54 

XVI. Deviations per judgment._ 54 

XVII. Deviation according to amount 55 

XVIII. Average deviations for 56 prospective judges in two tests 56 

XIX. Scores in form of a fifth grade class given by three judges scoring 

independently 58 

XX. Distribution of individual scores in terms of deviations from median 

scores on each sample 60 

XXI. Average deviation per sample for 60 judges 61 

XXII. Average deviation per class score for twenty groups of scorers 64 



LIST OF FIGURES 



PAGE 

I. Sample steps from the scales, in form, movement and spacing.... 8 
II. City wide grade medians in form, movement, spacing and rate of 

writing 15 

III. Sample A, illustrating the typical product of the better half of the 

upper eighth grade. — . 16 

IV. Sample B, illustrating the typical product of the upper eighth 

grade 16 

V. Sample C, illustrating the typical product of the poorer half of the 

upper eighth grade 17 

VI. Number of pupils writing at various rates 19 

VII. Medians — upper and lower quartiles for each grade in rate of writ- 
ing 20 

VIII. Class medians in rate of writing 21 

IX. Medians — upper and lower quartiles for each grade in form...-. 24 

X. Class medians in form 25 

XI. Medians — upper and lower quartiles for each grade in movement... 27 

XII. Class medians in movement .— 28 

XIII. Medians — upper and lower quartiles for each grade in spacing 30 

XIV. Class medians in spacing ;. 31 

XV. Average speed of writing in letters per minute for each scale step 

in form 33 

XVI. Average speed of writing in letters per minute for each scale step 

in movement .-. 36 

XVII. Average rate of writing in each grade for each step on the scale in 

spacing 38 

XVIII. Relation of class scores in quality and in speed for selected schools 40 

XIX. Relation of class scores in quality and in speed for selected schools.. 42 

XX. Relation of class scores in quality and in speed for selected schools.. 43 
XXI. Difference between 8B median and median scores for clerical 

groups — form, movement, spacing, speed.- 46 

XXII. Tentative grade standards 48 

XXIII. Tentative grade standards. 49 

XXIV. Supervisory graph showing grade standards :... 54 

XXV. Supervisory graph showing grade standards — twelve 8B grades 

in different schools 55 

XXVI. Supervisory graph showing grade standards — five 6B grades in 

one school 55 

XXVII. Total deviations of three judges 59 

XXVIII. Deviations from medians — 2259 judgments 63 



INTRODUCTION 

The present study represents one of a series of steps taken in 
New York City to establish definite goals of attainment in penmanship. 

On May 7, 1914, Dr. William H. Maxwell, City Superintendent 
of Schools, appointed a committee of teachers of penmanship to 
advise the Board of Superintendents as to (1) a imiform type of 
letters to be taught in all the schools; and (2) to formulate instruc- 
tions to teachers as to the teaching of muscular movement penman- 
ship. Subsequently in February, 1915, the Board of Education, upon 
the recommendation of the Board of Superintendents, adopted a 
uniform style of letters to be taught in all the city schools and also 
authorized the teaching of the muscular movement method of writ- 
ing which had been tried out in a number of schools for several years 
previous. 

The next step taken was the construction of a scale from the 
product of this system of penmanship. This was tmdertaken at the 
request of Acting Superintendent of Schools Straubenmuller by 
Messrs. Lister and Myers, Instructors in the Brooklyn Training 
School for Teachers. The resulting scale was officially adopted by 
the Board of Education in February, 1918. 

The setting up of grade norms for each of the elements measured 
by the scale was the aim of a study undertaken by the Bureau of 
Reference, Research and Statistics in June, 1919, and is the subject 
of this report. 

The grade standards set up as a result of the study were recently 
approved by the Board of Superintendents for adoption as part of 
the course of study and syllabus in penmanship. 

Inasmuch as the results of the study were reported upon in the 
December, 1920, nimiber of the Journal of Educational Research, 
it was originally decided not to issue the report as a publication of 
the Bureau. Repeated requests for the report, coupled with the 
adoption of the standards recommended, have led to its publication 
at this time. 

Acknowledgment is herewith made of the assistance rendered 
by Mr. Lister, Instructor of Penmanship in the Brooklyn Training 
School for Teachers, by Mr. Hugo Newman, Principal of the New 
York Training School for Teachers, and by Dr. Hamilton and Miss 
Scheuerman, Instructors in the latter named school. Without their 
untiring efforts in the training of the judges, who were training school 
students, and in the scoring of the papers the siu*vey would have 
been impossible. 



I. THE NEW YORK PENMANSHIP SCALE 



1. Characteristics 

The New York City Penmanship Scale possesses certain char- 
acteristics which distinguish it from the scales that preceded it. In 
the first place it is a scale constructed from the product of the sys- 
tem of penmanship it is intended to measure. 

The second characteristic of the scale is the fact that it is analy- 
tic. In judging ability in penman.ship there are so many things to 
be considered that a scale based on general merit only is of little 
assistance to the average teacher. The scale should help the teacher 
to look for the essentials in judging a given specimen of writing. 
Legibility, ease in writing or freedom of movement, good letter forma- 
tion, uniformity of size, uniformity of slant, clear and uniform spac- 
ing, neatness and an easy, fluent appearance, all these make up the 
value of writing. *"A scale by which each of these qualities must be 
estimated or judged individually would be too complicated to be 
practical. But it has seemed possible and practicable to group most 
of these qualities under three headings and thereby make a scale 
that will enable teachers to look for distinct qualities when grading 
specimens of penmanship. This should also enable the teacher to 
discover where the penmanship of her class is weak and to point 
the way to improvement; in other words, to analyze her product." 

"With this idea in mind it was decided to select and arrange 
specimens under three distinct headings. Form, Movement and Spac- 
ing, thereby making what might be termed a triple scale. 

"Under the caption Form, it was decided to consider accuracy 
in letter formation, with the standard letter forms adopted for the 
schools of New York City as the basis, imiformity of size, and regu- 
larity of correct slant. 

"Under Movement, the specimens were judged as to quality 
of line. As is well known to students of penmanship, heavy, tremu- 
lous and broken lines are evidence of either finger movement or mus- 
cular movement that is too slow and deliberate to produce skill; 
and clear-cut, smooth lines are evidence of the use of the easy-flowing 
muscular movement that is desired. 



♦Bulletin No. 3, Brooklyn Training School for Teachers, The New York City Penmanship 
Scale, by C. 0. Lister, January, 1919. 



''Under Spacing, the writing was judged as to correct and uni- 
form spacing between letters, between parts of letters and between 
words." 

t 
2. Construction of the Scale 

*"The scale represents the average judgment of twenty-one 
teachers and penmanship experts in the muscular system of penman- 
ship, and four psychologists. From nine schools of Greater New 
York, representative of the best, medium, and poorest product of the 
muscular system of penmanship, 3,550 specimens were selected 
from at least one entire class of each grade from 3'B to 8B inclusive. 
Each specimen represented one trial from dictation." 

"The specimens from each grade were classified into four piles 
by the writers on the basis of general merit and each pile was thor- 
oughly mixed with its corresponding pile of the several grades. Then 
on the basis of chance three hundred specimens were selected so that 
practically the same number was drawn from each pile. According 
to written instructions each of the twenty-five judges ranked these 
specimens in eight 'piles on the basis of equal intervals in merit. 
Accordingly, each judge ranked the three hundred specimens three 
times, namely, as to form, spacing and movement. 

"On the basis of the average rank assigned each speqimen, the 
best and the poorest were selected as the top and the bottom of 
the scale. Therefrom the exact numerical rank which the other six 
samples should have was determined. The specimens whose average 
ranks are the same as these determined positions, or are nearest 
them were selected. Without exception all the samples on the scale 
are less than 0.1 from the determined position." 

Figure 1 illustrates the resulting scale. The scale consists of 
twenty-four specimens arranged in parallel columns,- — eight under 
Form, eight under Movement, and eight under Spacing. The scale 
values of the specimens under each element are 90, 80, 70 — 20. 
Four specimens under each element are reproduced below. These 
represent alternate steps beginning with 90. 

*An Analytic Scale of Handwritiag. by 0. C. Lister and G. C. Myers, Journal of Educa- 
itonal Psychology, October, 1918. 







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II. MEASURING PRESENT ACHIEVEMENTS IN PEN- 
MANSHIP 

As a first step in the determination of grade standards for the 
New York Scale, the Bureau undertook to measure present achieve- 
ments in penmanship in the schools. Penmanship tests were con- 
ducted in fifteen schools selected as representative of the whole sys- 
tem.- 

1. Conduct of Tests 

Uniformity of Conditions. While it is comparatively simple to 
secure samples of the children's writing, particular care was taken to 
have uniform conditions obtain. The tests were given by thirty 
students from the New York Training School for Teachers who had 
had the coiu*se in educational measurements given in that school 
and also the normal course in muscular movement penmanship. 
These girls were familiar with the various scales in penmanship and 
had some experience in the conduct of standard tests. In addition 
they received practice in giving this penmanship test in accordance 
with formulated instructions, considerable attention being given to 
the question of "timing." 

The children in the classes to be tested memorized on the day 
before the test the sentence that was used, viz., "One must exercise 
in work and in play." In the lower grades the class teachers gave 
attention to the word "exercise" in order to insture familiarity with its 
spelling by each child. The test consisted of writing repeatedly the 
above-mentioned sentence for two minutes. The class teachers took 
no part in the testing, although present in the rooms at the time. 

The test was given in 500 classes, involving 18,000 children, in 
grades 4A to 8B. For purposes of this report about twelve thousand 
specimens were scored in full. 

The scoring was done by training school students. The methods 
employed, the training of the judges and the reliability of the scor- 
ing that resulted are discussed in a later section of the report. (See 
Appendix A.) 

2. General Results 

Table I shows the median scores obtained by each grade group 
throughout the city in each of the elements measiu-ed by the scale, 
form, movement, spacing and in rate of writing. 

14 



TABLE I— CITY-WIDE MEDIAN SCORES BY GRADES FOR FORM, MOVEMENT, 

SPACING AND RATE 





FOBM 


MO'/EMENT 


Spacing 


Rate 




Grades* 










No. of 












Pupils 




Median 


Median 


Median 


Median 




8B 


61 


62 


65 


82 


988 


8A 


57 


61 


63 


83 


1,117 


7B 


54 


56 


59 


79 


1,225 


7A 


55 


56 


59 


78 


1,327 


6B 


54 


56 


58 


72 


1,481 


6A 


51 


53 


56 


69 


1,414 


5B 


49 


49 


54 


69 


1,327 


5A 


45 


45 


51 


66 


1,529 


4B 


43 


43 


48 


63 


1,110 


4A 


38 


40 


48 


58 


24] 


City 


51.3 


52.9 


56.4 


72.5 


11,759 



* The letter A designates the first half of the school year; the letter B the second half. 



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Figure 2 shows the above graphically. The vertical axis shows 
the rank on the scale and also indicates the rate in letters per min- 
ute. The horizontal axis shows the grades. For the city as a whole 
the median score for all the pupils tested is (without regard to grade) 
51.3 in form, 52.9 in movement and 56.4 in spacing. This means 
that 50 percent, of the pupils tested, without regard to grade, obtained 
these scores or better. The table also shows that 50 percent, of all 
the pupils wrote at a rate of 72.5 or more letters per minute. 



15 



In order to show concretely the product of the schools in pen- 
manship the following specimens of pupils' writing are presented. 
The size of the writing is somewhat reduced in the reproduction. 



FIGURE 3. 



SAMPLE A, ILLUSTRATING THE TYPICAL PRODUCT OF THE 
BETTER HALF OF THE UPPER EIGHTH GRADE 




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Form 


Movement 


Spacing 


Speed 


Sample A 


70 
69 


70 
70 


70 
71 


92 


Q3 


94 







This sample was equaled or surpassed by 25 percent, of the pupils of the upper 
eighth grade. 



FIGURE 4. SAMPLE B, ILLUSTRATING THE TYPICAL PRODUCT OF THE 
UPPER EIGHTH GRADE 







Form 


Movement 


Spacing 


Speed 


Sample B 

Median 


60 
61 


60 
62 


65 
63 


82 
82 







This sample was equaled or surpassed by 50 percent, of the SB group. 

16 



Sample A, Figtire 3, is the writing of an 8B boy, written at the 
rate of 92 letters per minute and judged to be of quality 70 in form, 
70 in movement and 70 in spacing. It represents approximately 
writing that was equaled or surpassed by 25 percent, of the pupils 
in the 8B grade. The point in the 8B distribution which includes 
25 percent, of the pupils, counted from the upper end, is called the 
third quartile. The third quartile is located at 68.8 in form, 70 in 
movement, 71 in spacing and 94 in speed. 

Sample B, Figure 4, is the writing of an 8B girl, written at the 
rate of 82 letters per minute and judged to be of quality 60 in form, 
60 in movement and 65 in spacing. It approximately represents 
median performance for the 8B grade, that is writing which was 
equaled or surpassed by 50 percent, of the 8B pupils. The median 
for the 8B is 61 in form, 62 in movement, 63 in spacing and 82 in 
speed. 

The 25 percent, point in the distribution calculated from the lower 
end is called the lower quartile or first quartile. In the 8B grade 
■this was 53 in form, 53 in movement, 58 in spacing and 68 in speed. 
Sample C, figure 5, represents an 8B pupil's writing which approxi- 
mates these values; 25 percent, of the 8B pupils wrote as poorly or 
worse than this sample and at a slower rate. 

FIGURE 5. SAMPLE C, ILLUSTRATING THE TYPICAL PRODUCT OF THE 
POORER HALF OF THE UPPER EIGHTH GRADE 





Form 


Movement 


Spacing 


Speed 


Sample C 


55 
53 


50 
53 


55 
53 


64 


Qi 


68 







This sample was equaled or surpassed by 75 percent, of the pupils of the upper 
eighth grade. 

The above samples may be used also to illustrate the results 
obtained in the other grades. 



17 



3. Rate of Writing 

Examining the data more in detail let us consider first the rate 
of writing. The specimens of penmanship obtained from the test 
were scored for rate of writing by some of the training school pupils 
who had served as examiners. In such scoring they made use of 
mimeographed copies of the test sentence upon which there was a 
coimt of the letters. The nimiber of letters written for two minutes 
thus determined was reduced to the rate per minute. 



TABLE II— DISTRIBUTION OF INDIVIDUAL SCORES FOR RATE OF 
WRITING 



Letters 


G CADES 


Total 


Percent, 
of 


Cumu- 


per 






















lat've 


minute 


4A 


4B 


5A 


5B 


6A 


6B 


7A 


7B 


8A 


8B 




total 


percent. 


150 










1 






5 






6 


0.05 


0.05 


140 
















6 






6 


0.05 


0.1 


130 








1 





1 


2 


3 


2 


3 


12 


0.1 


0.2 


120 






3 


4 


6 


14 


18 


27 


21 


15 


108 


0.9 


1.1 


110 


1 


1 


2 


7 


8 


21 


32 


29 


53 


32 


186 


1.6 


2.7 


100 





13 


23 


32 


56 


101 


115 


98 


119 


92 


649 


5.5 


8.2 


90 


1 


41 


105 


116 


117 


172 


200 


219 


224 


188 


1,383 


11.8 


20.0 


80 


7 


69 


158 


148 


152 


181 


217 


210 


185 


192 


1,519 


12.9 


32. y 


70 


38 


216 


341 


329 


325 


324 


367 


282 


256 


189 


2,667 


22.7 


65.6 


60 


63 


323 


363 


320 


327 


286 


223 


214 


149 


130 


2,398 


20.4 


76.0 


50 


51 


198 


221 


153 


186 


150 


99 


72 


58 


- 69 


1,257 


10.7 


86.7 


40 


61 


170 


178 


151 


177 


144 


39 


44 


40 


60 


1.064 


9.0 


95.7 


30 


16 


69 


101 


52 


49 


72 


12 


15 


10 


14 


410 


3.5 


99.2 


20 


3 


9 


28 


11 


8 


15 


3 


1 




3 


81 


0.7 


99.9 


10 




1 


6 


3 


2 











1 


13 


0.1 


100.0 


Total 


241 


1.110 


1,529 


1,327 


1,414 


1,481 


1,327 


1,225 


1,117 


988 


11,759 


100.0 









Table II gives the distribution of the scores of all pupils by grades. 
The next to the last column of Table II shows the percent, of all 
pupils that wrote at each rate of speed. Such data reduced to a 
millenar}^ basis in figure 6 shows that out of every thousand pupils 
tested 1 wrote at the rate of 140 or more letters per minute, 1 at 130 
or more letters, 9 at 120, 16 at 110, and so on down to 35 who wrote 
less than 40 letters, 7 less than 30 and 1 less than 20 letters per 
minute. 

The last column on Table II shows the cumulative percent, 
ranging from the top downward. It shows, for instance, that 82 
out of every thousand or 8.2 percent, wrote 100 or more letters, that 
20 percent, wrote 90 or more, that 32.9 percent, wrote 80 or more, 
and 55.6 percent, wrote more than 70 letters per minute. The 
standard speed set up by Ayres for the eighth year is 80 letters, which 
is equaled or exceeded by 32.9 percent, of all the pupils. Two him- 
dred pupils out of every thousand or 20 percent, equal or surpass the 



18 



standard rate of 90 letters set up by Freeman for the eighth year. 
The above disregards grade distinctions and shows that the New York 
pupils are rapid writers. [^ _. 

. FiauRF 6 







fslllMSER 


Of Pupils WRiTiNfi At Various 


Rates 








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1 


7 


















16 


9 


, 


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10 


20 


30 


40 


SO 


60 


70 


80 


90 


100 


no 


liO 


130 


11-0 



Table III, which follows, gives the median rate for each grade, the 
rates for the upper quartiles and the lower quartiles and the range of 
the middle 50 percent, of the group. It also gives, for comparative 
purposes, standards set up by Ayres and by Freeman and the results 
obtained in the Cleveland Siu^ey. 

TABLE III— GRADE MEDIAN RATES, UPPER AND LOWER QUARTILES 



Grades 


4B 


5A 


5B 


6A 


6B 


7A 


7B 


8A 


8B 


M 
Q^ 


73.0 
63.3 
51.4 


77.3 
66.3 
53.1 


79.3 
69.1 
57.5 


79.8 
68.7 
56.3 


86.7 
72.2 
59.3 


91.8 

77.8 
68.0 


93.7 
79.4 
6S.1 


95.4 
82.5 
70.9 


94.4 
81.5 
67.7 


Range 

Middle 

oOpercent. 


21.6 


24.2 


21.8 


23.5 


27.4 


23.8 


25.6 


24.5 


26.7 


Freeman 

Standards 

Ayrpa 

Standards 

Cleveland 

Survey- 


56 
56 


65 
64 
60 


72 
70 
70 


80 
76 
76 


90 
80 
80 



19 



Figure 7 shows the above data graphically. It appears that the 
median rate of writing increases irregularly from grade to grade 
rising from 63 letters per minute in the 4B grade to 82 in the second 
half of the 8th year. * There is no gain shown in the 6A grade over 
the 5B while in the 8B the rate is slightly lower than that of the 
grade below. The greatest gain appears in the 7A. 



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New York children are by no means slow writers. Their rates 
are higher than the scores obtained in other surveys and exceed in 
all years the standards set up by Ayres. With the exception of the 
last three half years the median scores are higher than the standards 
fixed by Freeman, which were based upon the average of the better 
half of the schools tested by him. 



* The data obtained for the 4A grade will be disregarded because of the small number of 
pupils tested. 



20 



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Figure 8 shows by grades the medians for each class in rate of 
writing. Each square represents a class and the figure within the 
square is the median score attained by that class. The scores are 



21 



arranged in intervals of five. For instance, in the top figure, the 
4B grade, there were three classes with medians of 50, one with 51, 
one with 53, and so on. The slowest class obtained 50 and the most 
rapid 78. The classes in this grade are closely bunched. In the 5A 
the slowest class score is 32 while that of the most rapid is 88, more 
than twice as large. It is to be noted that the majority of the classes 
are above 60. 

As we go up through the grades the central tendency moves 
toward the right and the lower scores drop off. The diagrams show 
the great variability in performance by classes within the same grade, 
in many cases within the same school. Grade distinctions have little 
significance when one considers the marked overlapping that is 
revealed. In each grade quite a large number of classes could be 
replaced by an equal number of classes from a higher or from a lower 
grade without seriously affecting the grade distribution as far as 
speed or rate of writing is concerned. 

It is to be borne in mind that we are dealing not with scores of 
individual pupils but with class groups. The variability cannot be 
attributed to individual differences in ability but must be charged 
to lack of imiform grade standards in oiir instruction. While such 
conditions are significant they are not surprising and have been shown 
in a number of studies in other school systems jand in other subjects 
besides penmanship. 

Some index of the degree to which the grades overlap is obtained 
by comparisons of the upper quartiles of different grades with the 
median rate of higher grades (see Table III). For instance, the 
upper quartile for 4B is 73.0 which is a higher rate than the median 
of the 6B grade, 72.2, four grades above. In other words, 25 percent, 
of the 4B children write faster than 50 percent, of the 6B children. 
Likewise^25 percent., at least, of the 5A children write a good deal 
faster than 50 percent, of the 6B grades; 25 percent, of the children 
in the 5B attain a speed of 79.3 and exceed the rate of 50 percent, of 
the 7B children, and 25 percent, of the 6B group write faster than 50 
percent, of the eighth year group. 

Comparing the lower quartiles of different grades with the 
median of lower grades we see, for instance, that in the 8B grade 
25 percent, of the pupils write more slowly than 50 percent, of the 
5B grade, six grades lower. Similarly 25 percent, of the 6B grade 
write at a rate which fails to equal the median of the 4B grade, four 
grades below. 

Reverting to the grade distributions again (Table II) which 
shows the individual scores in each grade, we see even greater vari- 
ability between the rates of writing of children within the same grade. 
In all grades practically the same range is required to express the 

22 



rates obtained by the individual pupils. In the 4B the rate varies 
from that of one pupil who wrote less than 20 letters per minute 
to one who wrote more than 110 letters per minute. In the 
7B grade the rates range from that of the slowest pupil who 
wrote at a rate of less than 30 up to five pupils who exceeded 
150 letters. 

As far as rate of writing is concerned grade distinctions mean 
nothing. To say a pupil is in the 8B indicates little as to his speed of 
writing. He may write very fast or he may write at a slower rate 
than the average of the 4B pupils. 

The condition revealed indicates an absolute lack of grade 
standards. It does not necessarily mean that emphasis has been 
put upon speed but rather does it indicate that no particular atten- 
tion has been paid to controlling the rate at which children write. 
The children who began as slow writers probably continued as slow 
writers throughout the grades, with only such increase as may 
come from increased age or maturity. The fast writers in the 
lower grades probably continue likewise to write at a rapid rate 
throughout. 

While writing of a good quality is a prime requirement, instruc- 
tion should also seek to improve the rate of writing, particularly of 
the slower writers. Less than 80 letters per minute is slow writing. 
The presence of n-umbers of pupils in the last year of the course who 
fail to attain a speed of 60 letters per minute indicates the failure 
of OMT instruction to give pupils about to leave school writing habits 
which will meet the requirements of the outside world. . The presence 
of pupils in all grades who write at very rapid rates again indicates 
the need of control so that the quality of the writing of such pupils 
is not sacrificed for the sake of speed. Rapid writing must be accom- 
panied by satisfactory quality. 



4. Quality of Writing 

(a) FORM 

How well do New York pupils write? The specimens of writing 
were scored for form, movement and spacing by means of the New 
York Penmanship Scale. 

Under "Form" were considered the letter formation, uniformity 
of size and regularity of correct slant. 

Table IV shows for form the medians, the upper and lower 
quartiles and the range of the middle 50 percent, in each grade. 
Figure 9 shows these figures graphically. 

23 



TABLE IV— GRADE MEDIANS, UPPER AND LOWER QUARTILES IN FORM 



Grade 


4A 


4B 


5A 


5B 


6A 


6B 


7A 


7B 


8A 


8B 


City 


Median 


47.1 
37.9 
30.0 


49.8 
43.2 
35.8 


53.4 
45.4 
38.3 


58.2 
49.2 
40.9 


59.5 
50.5 
42.4 


62.3 
53.7 
45.2 


63.6 
54.5 
45.6 


62.9 
54.0 
45.4 


67.8 
57.0 
47.7 


68.8 
60.8 
52.6 




Range of Mid- 
dle 50 percent. 


17.1 


14.0 


15.1 


17.3 


17.1 


17.1 


18.0 


17.5 


20. 


1 


16.2 




Grade interval 
between medians 


6.3 


2.2 


3.8 


1.3 


a 


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0.8 


0.5 


3.0 


3.8 





The grade medians for form show a sHght irregular progress from 
grade to grade, varying from 37.9 in 4A to 60.8 in grade 8B. 
Improvement is shown from the 4A up to the 6B. In the 6B, 7A 
and 7B the form remains practically on a level. In the 8A and 8B 
the medians show a gain. The average grade interval is but 2.5 
points or about one-fourth of a step on the scale. The total differ- 
ence between the 4B and 8B medians is a little more than 20 points 
or two steps on the scale. 



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24 



In most of the grades the range of the middle 50 percent, of the 
group approximates the total median improvement between the 
lowest and highest grades. In other words, considering only the 
middle 50 percent, of the children we find there is approximately as 
great a difference in any grade between the upper and lower quartiles 
as there is between the medians of the 4B and the 8B grade. 

The results by classes in each grade are presented in Figure 10. 
Each square shows a class and the figure within the square repre- 
sents its median score. The 35 classes tested in the 4B, it will be 
seen in the top diagram, range from 30 for the lowest up to 57 for 
the highest. The great majority of classes are found in the "forties." 
The 5A grade shows greater variation. Here the range is from 33 up 
to 66. The class with the lowest score does only half as well as the 
highest class. The central tendency here is in the group 45 to 49. 



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The advance from grade to grade is seen b}^ the gradual shifting 
of the central tendency to the right, that is toward a higher score 



25 



and also by the falling away of the lower scores in the upper grades. 
At the same time the variation in class performance is typical of each 
grade and the overlapping of grades is quite marked. The over- 
lapping of grade and grade may be roughly indicated by a compari- 
son of the upper quartile of one grade with the medians of higher 
grades, and by a similar comparison of the lower quartile with the 
medians of lower grades. Table V shows such a comparison. 



TABLE V— COMPARISON OF QUARTILES WITH MEDIANS TO SHOW OVER- 
LAPPING 





Medians 






Lower 
Quartiles 


4A 


4B 


5A 


5B 


6A 


6B 


7A 


7B 


8A 


SB 


Upper 
Quartiles 


37 9 


43 2 


45 4 


49 2 


50 5 


53.7 


54.5 


54 


57.0 


60.8 


4A 30 




,,, 


2 3 


0.6 
4.2 


2 9 


4 5 
5.8 


3.7 
5.0 

J.S 


4-2 
5 5 
8 3 
.0 


1.2 
2 5 

5 3 

6 6 
5 9 


1.5 
1.5 
2.8 
2.1 
7 


47.1 
49.8 
53.4 
.58.2 
59.5 
62.3 
63.6 
62.9 
67.8 
68.8 


4A 


4B .35.8 


—2.1 


4B 


5A 38 . 3 


— 4.9 
—2.3 

— 0.8 


5A 


5B 40.9 


—3 6 
—3 
—0.2 


5B 


6A 42.4 


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—4 .? 
—3 6 
—3 8 
—1.5 


6A 


6B 45.2 


—3.6 
— 4 6 
—5 1 

—2.8 


6B 


7A 45.6 


—8 1 
—8 3 
-6.0 
— 1 1 


7A 


7B 45.4 


—9.1 
—6.8 
— 1 9 


7B 


8A 47.7 


—6.3 
— 1 4 


8A 


8B 52.6 


-^.4 


8B 



In Table V the medians for the various grades are given across 
the top, the lower quartile is shown in the left hand column, and the 
upper quartile in the last colimm on the right. 

The figures to the right of the heavy line show how much the 
upper quartile of a given grade exceeds the median of the grades 
above. The figures to the left show how much the lower quartile 
of a given grade falls below the median of lower grades. For instance, 
the median of the 5B grade is given at the top as 49.2, the lower 
quartile is given at the left as 40.9. Reading horizontally across 
from 5B to the left of the heavy line shows that the lower 25 percent, 
of the 5B groups fails to reach the median of the 4B grade by 2.3 
points and the median of the 5A grade by 3.6 points. The figiures 
on the same line to the right of the heavy line show that the upper 
quartile of the 5B exceeds the 6 A median by 7.7 points, the 6B 
median, two grades above, by 4.5 points, the 7A median by 3.7 points 
the 7B median by 4.2 points, and that of the 8A, five grades above, 
by 1.2 points. Similarly for the other grades. In the 8B we find 
that the poorest writers do not write as well as the average writers 
of the 6B, several grades below. 



26 



(b) MOVEMENT 

Under the element of movement was considered the quahty of 
line on the assiimption that the character of the movement would be 
indicated by the quality of line. Table VI shows for each grade the 
medians, the upper and lower quartiles and the range of the middle 
50 percent, in the element of movement. Figure 11 shows these 
data graphically. 



TABLE VI— GRADE MEDIANS, UPPER AND LOWER QUARTILES IN 
MOVEMENT 



Grade 


4B 


5A 


5B 


6A 


6B 


7A 


7B 


8A 


8B 


City 


Q^ 

Median 

Q^ 


53.1 
43.3 
35.7 


54.6 
44.8 
36.4 


59.7 
49.3 
39.8 


63.3 
52.9 
43.1 


65.3 
56.1 
46.3 


65.6 
56.0 
45.9 


64.7 
55.7 
46.4 


69.9 
60.8 
49.2 


69.6 
62.0 
52.9 


63.5 
52.9 

42.2 


Range of 
middle 50 
percent. 


VIA 


18.2 


19.9 


20.2 


19.0 


19.6 


18.3 


20.7 


16.7 


21.3 


Inter\ 
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27 



The grade medians for movement show an irregular progress 
from grade to grade rising from 39.9 in 4A to 62.0 in 8B. The extent 
of improvement is slight. In the 7 A and 7B there is a slight loss 
which is made up by the gain of 5 points in the 8A, the largest grade 
increase. The average gain per grade is but 2.5 points or one-fourth 
of a scale step. The total difference between the 4A and 8B medians 
is but 22 points or a little more than two steps on the scale. 

Here again, as in form, the range of the middle 50 percent, of 
the group in most of the grades is almost as great as the difference 
between the medians of the highest and lowest grades. 



Pi G 1 1 p F X. 1 1 












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Figure 12 shows by grades the distribution of class scores. In 
the 4B grade, for instance, out of the thirty-five classes tested the 
lowest class received the score of 29 and the highest class scored 53. 
The greatest number of classes are concentrated in the forty and 
forty-five columns. The range of class scores is quite wide in all 



28 



grades. In the 8B it is narrowest. The variability in the perform- 
ance of the classes and the overlapping of the grades are readily 
apparent. The situation in movement is the same as that revealed 
in form. 

A comparison of the upper and lower quartiles shows likewise 
the extent to which grade distinctions are without significance in 
this subject. The upper quartile of the 4B exceeds the median of the 
6A, three grades above. The upper quartile of the 6A exceeds the 
median of the 8B and so on. On the other hand, the lower quartile 
of the 8B is just equal to the median of the 6A and is less than the 
median scores of the intervening grades. The lower quartile of the 
8A is lower than the median of the 5B. In the same way 
the lower 25 percent, of the 6 A group write worse than 50 percent, 
of the 4B. 

(c) SPACING 

Spacing includes the elements of uniform spacing of letters, of 
parts of words and of words. Table VII gives the city wide median 
scores for each grade group in this element. It also shows the upper 
and lower quartiles and the range of the middle 50 percent. 



TABLE VII— GRADE MEDIANS, UPPER AND LOWER QUARTILES IN SPACING 





Grade 


4B 


5A 


5B 


6A 


6B 


7A 


7B 


8A 


8B 


City 


Q^ 

Median 

Q^ 


56.3 
47.7 
40.6 


58.4 
50.5 
42.2 


62.5 
54.0 
45.0 


64.6 
56.2 
48.2 


65.9 
57.7 
50.8 


66.9 
58.7 
51.0 


66.6 

58.7 
51.6 


70.7 
63.2 
54.3 


71.6 
64.8 
57.5 


65.5 
56-4 
47.5 


Range of 
middle 50 
per cent. 


15.7 


16.2 


17.5 


16.4 


15.1 


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15.0 


16.4 


14.1 


18.0 



Interval 
between 
grade 
medians . 



+2.8 



+3.5 +2.2 



+ 1.5 



+ 1.0 



0.0 



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+1.6 



Figure 13 shows the same data graphically. With the excep- 
tion of the 7B grade the medians of each grade show an increase, 
from 47.7 for the 4B to 64.8 for the 8B. The total increase between 
the 4B and the 8B grades is but 17 points, less than two steps on the 
scale. This is approximated by the range in scores of the middle 
50 percent, in almost each grade. The average grade increment is 
a very small part of a scale step. 



29 



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Inspection of the quartile and the median scores, as with the 
other elements, again shows what Httle significance grade distinctions 
possess. The upper 25 percent, of the 5A group do better than the 
lower 25 percent, of the 8B grade. Fifty percent, of the 8B pupils 
do poorer than 25 percent, of the 6B. Twenty-five percent, of the 
8B fail to get as high scores as 50 percent, of the 6B, four grades 
below. 

The above data are for the grade groups throughout the city. 
For the individual classes the scores are shown in Figure 14. As 
in the other elements the marked characteristic is the variation 
between classes, in many cases as great a difference being present as 
was found between the 4B and the 8B grade groups for the whole 
city. Again, also the overlapping of the grades shows up in marked 
degree. Such data are class scores and not the scores of individuals. 

4. Relation op Speed and Quality 

The previous sections of the report considered the results in 
terms of speed and of the elements of quality alone. A very import- 
ant question to be considered in examining the results is the relation 
between quality and speed. It is possible for us to set up grade 
norms for the various elements of quality, norms which may be 
achieved but at the expense of speed. At the same time we may 
establish certain norms for speed which also may be attained 



30 









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Grace: 6A 


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but at the expense of good form or other characteristics of quaHty. 
Satisfactory quality must be attained but must be accompanied by 
satisfactory rates of v^n-iting. 

From Table II which showed the medians in each characteristic 
of quality and also in rate, it may be noted that speed increased 
with one or two exceptions from grade to grade. At the same time 
the median scores in form, in movement and in spacing also increased 
from grade to grade. There was a certain degree of correspondence 
as far as the whole grade groups were concerned between the median 
speed and the median scores in quality from grade to grade. 

Does such relation hold within the grades? In order to deter- 
mine this the average speed was determined for each scale score in 
each grade in form, movement and spacing. Table VIII shows for 
each grade the average speed at which each quality in form was 
written. 



31 













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32 



f^lCt-lRE. XV 



AtE SpEI- 

Letter.^ 



D OfNA/r 

Per Mini 




Figure 15 shows graphically for each grade the data contained 
in Table XVII. The vertical axis represents speed in letters per 
minute. The horizontal axis represents ascending steps in form. 
From the diagram it will be noted that in the 4B grade, for instance, 
the pupils scoring 80 in form wrote at an average rate of 48 letters a 



33 



minute. On following the line toward the left it is seen that the 
rate for those scoring 70 in form was 49 letters per minute, for those 
scoring 60 the rate on the average was 59 letters, for those scoring 
50 the rate was 62 letters and so on. Similarly for the other 
grades. 

There appears to be a general tendency toward decrease 
of speed as form improved. In the 4B grade it will be noticed, how- 
ever, that the speed averaged fairly constant up to the 60 step and 
then declines rapidly for the upper ranges in form. Higher quality 
evidently is attained at the sacrifice of speed. In the 7th and 8th years 
also the speed shows quite a constant average from 50 steps upward. 
The higher rates of speed are accompanied by lower scores in form. 
Here it appears that the greater speed results in poorer form. 

Table IX shows similar data for the element of movement and 
is illustrated by figure 16. 

The same general tendency toward a decrease in quality with 
increased rate of writing is revealed. At the same time it appears 
in some of the grades that with the intermediate ranks or steps in 
movement, the averages for speed remain fairly constant. For 
instance, in the 8B grade for the scale step from 30 to 80 the rates are 
85, 83, 81, 79, 80, 78. In the 8A for the steps from 40 to 70 in move- 
ment the rates are 84, 84, 80, 83. In the 4B also the rates of speed 
are practically the same for all ranks on the scale except the very 
extremes. For the steps from 30 to 60 inclusive the rates are 64, 
63, 62, 60. While an inverse relationship is shown it does not appear 
to be very large. 



34 





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35 



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gure XVI 




Table X and Figure 17 show similar data for the element of 
spacing. The data for spacing show in general an inverse relation 
between speed and spacing with an intermediate area from ranks 40 
to 60 where no correlation is apparent. 



36 









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"Writing 

FT'R FftC.H 




80 go 



To obtain a clear and more exact determination of the relation 
existing between the elements of speed and form, movement and 
spacing, than was afforded by the analysis presented in the preceding 
section, the degree of correlation between the several characteristics 
or elements was computed. Instead of treating all of the data 
involved in the scores of the 12,000 pupils, two sets of 1,000 specimens 
each were selected by a process of sampling. 



38 



The product moment formula was used in the computation of the 
coefficient of correlation with the following results: 



TABLE XI— COEFFICIENTS OF CORRELATIONS BETWEEN THE SEVERAL 

ELEMENTS 



Elements 



1st Sampling 



P. E. 



2d Sampling 



P. E. 



Form and movement 

Form and spacing 

Movement and spacing. 

Speed and form. 

Speed and Movement- 
Speed and spacing 



+ .75 
+ .73 
+ .72 
—.056 

— .036 

— .013 



.0093 

.0094 

.0101 

.02 

.02 

.0213 



+ .749 
+ .738 
+ .716 

— .054 

— .029 

— .016 



.0092 

.0097 

.0103 

.02 

.02 

.0213 



The correlation between speed and the elements of form, move- 
ment and spacing is negligible. The fact that the probable error 
is as large or larger than r indicates the imreliability of our result. 
It appears then that there is little relation between speed and the 
different elements of qualtiy in writing. The fast writers write a 
good hand as well as the slow writers. The good writers write 
rapidly as may also the poor writers. 

In the case of the other elements a high degree of positive corre- 
lation is shown. This indicates that an increase in form would be 
accompanied by an increase respectively in movement and in spa- 
ing and vice versa. 



6. Relative Emphasis on Quality and Speed in Different 

Schools 

The results of our test already presented have clearly indicated 
the variability of achievement in the various classes and grades. 
It has been shown that there is apparently an absolute lack of uniform 
standards of achievement in the various grades and even among 
classes within the same grade. In this section data will be presented 
showing the relative emphasis placed upon speed and upon quality 
in some of the schools tested. 

In order to show the development in penmanship through the 
grades, the progress in quality and the progress in speed may be 
shown under one diagram. For quality the grade median scores in 



39 



form, movement and spacing were averaged to obtain a single score. 
The resulting curves would not be materially different if we were to 
take only one element at a time. 





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Figure 18 shows the progress from grade to grade in three 
selected schools. The horizontal axis shows speed. Distance to 
the right indicates progress in speed. The vertical axis measures 
quality and distance upward indicates progress in quality. In inter- 



40 



preting the diagrams we must bear in mind that the distance between 
the horizontal axes measures only ten points or one step on the pen- 
manship scale, and that distance between the vertical axes represents 
but ten letters. 

The top diagram of figure 18 represents a school which shows con- 
siderable progress in quality from the 4B to the 6B. The score in 
4B in quality is 44, in the 5A it is 48, in 5B, 56, in 6A, 57, and in 6B, 
59. At the same time it is apparent that no effort has been made to 
control the speed in those grades. The 5A grade shows a loss in 
speed of 11, the 5B makes a large gain. over the 5A, from 53 to 73. 
There is a further gain in the 6A and then a considerable loss in the 
6B, a drop from 77 to 63. The last two years show a gain in speed 
but with the exception of the 8B, a loss in quality from the level 
reached by the 6B. The course of study does not prescribe penman- 
ship in the last two years. This, together with the increased demands 
in the upper grades for rapid writing, may explain in part the situa- 
tion revealed. 

The middle graph in Figure 18 shows another instance of irregu- 
lar development. In this school the 4B scored 52 in quality and 72 in 
speed, the 5A scored 55 in quality, a gain of 3 points but only 63 in 
speed, a loss of nine letters. The 5B shows a drop in quality from 55 
to 45 but a gain in speed. The 6A makes up partly for the loss in 
quality by a gain of 8 points, scoring 53 which is below the 5A score. 
The 6B grade score shows a very large gain in speed but just equals 
the 5A in quality. From the 4B to the 6B the net result is a gain of 
only 3 points in quality. From the 7A on the curve turns sharply 
upward and the. apparent emphasis on quality results in a con- 
siderable gain, from 51 to 64, but is accompanied by only a slight 
gain in speed. The 8B with a score of 62 in quality and 88 in speed 
shows a loss in both but still reaches the 8B city median in quality 
and exceeds it in speed. 

The school represented in the diagram at the bottom of Figure 
18 shows an erratic course of development and indicates the lack of 
grade standards. The 4B and 5 A grades show relatively average 
quality and speed, the 5B and 6 A show an increase in quality with 
considerable loss in speed, the 6B shows an equal gain in quality 
and speed. The last two years gain in speed but fail to maintain or 
gain upon the level in quality reached by the 6B . 

Figure 19 presents graphs for two other schools which show the 
different emphasis placed upon speed and upon quality in the differ- 
ent grades. The standards of the teachers in the different grades 
within the same school are most variable. It indicates that the 
question of balanced development or progress in both speed and 
quality has not had the consideration of the principal. 

41 



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relative emphasis upon quality and speed. The middle diagram 
shows a school in which the emphasis has been placed solely upon 
quality with no attempt to control or improve the rate of writing. 
Taking quality alone for instance we see improvement from the 5A 
to 5B from 46 to 51, a very slight loss in the 6A, a sharp rise in the 6B 
to 57, a loss in the 7A of four points, a gain in the 7B of five points 
to a score of 58, a further gain of three points in the 8 A and of one 
intheSB. 



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43 



All the grades with the exception of the 7A are equal to or above 
the city wide medians in quality. The speed shows a general trend 
toward the left. With the exception of the 7A no grade equals the 
5A, the lowest grade (in this school) tested. The 5A with a speed of 
71 exceeds the city wide 5A median of 66 by five letters. The6A 
equals the grade median but all the other grades fall below their 
respective city medians. The school needs emphasis in speed, partic- 
ularly in the upper grades. 

The data presented above show the need and desirability of a 
study of grade standards in the several schools by the principals and 
teachers. 

From the data presented it is quite apparent that the control 
of the schools over the product in penmanship is anything but effec- 
tive. There is the greatest variability in achievement in the various 
classes of the same grade in different schools or between classes in 
the same grade within the same school. The median improvement 
from grade to grade is very slight and indicates how futile much of 
the instruction must be. The total improvement between the 4B 
and 8B grades is about two steps on the scale and this is equaled in 
most of the grades by the range of the middle 50 percent, of the 
pupils. The progress from grade to grade in most of the schools is 
uncertain and erratic. The situation is such that you can predicate 
practically nothing about the penmanship of an 8B pupil or even of an 
8B class. It might do as well as the 6B city average or it might not. 
The SB pupil might write as well as the 6B grade average with the 
speed of the 4B or even vice versa. 

The situation is just what might be expected from a lack of 
standards to guide the teacher in her instruction or the principal in 
his supervision. Without the control which standard measurement 
yields the development of skill in penmanship is bound to be erratic. 



44 



III. TENTATIVE GRADE STANDARDS 

1. The Degree oe Penmanship Ability Found in The Business 

World 

The end product of our school training is represented by the 8B 
pupil who is about to graduate. How well should a pupil in the 8B 
write? At what speed? Immediately we answer such questions by 
asking other questions. How well need he write? How fast need 
he write? We find our answers in the demands of society upon the 
pupil and in the needs of his later life. 

There have been a number of studies and investigations con- 
ducted to determine the degree of writing skill required by the out- 
side world in various lines of endeavor. Such studies however were 
reported in terms of the A3rres scale so that the results could not be 
used in setting up norms for the New York scale. An independent 
attempt was made to determine the degree of skill in the various ele- 
ments of handwriting, as measiured by the New York scale, that was 
to be found in clerical workers. The Bureau obtained under test 
conditions samples of handwriting of clerical employees in several of 
our large department stores. The group tested numbered 161, dis- 
tributed as follows: 98 salesclerks, 17 billers, 39 checkers, and 7 
clerks and bookkeepers. In all these positions legible rapid writing 
was considered essential. 

Table XII presents the median scores in each element for each 
of the above groups in comparison with the median scores of our 
8B pupils. 

TABLE XII— median SCORES OF GROUPS OF CLERICAL EMPLOYEES IN 
DEPARTMENT STORES 





Num- 
ber 


FOKM 


Movement 


Spacing 


Speed 


Group 


Med. 


Dif. 

from 
8B 


Med. 


Dif. 

from 
SB 


Med. 


Dif. 

from 

SB 


Med. 


Dif. 

from 
SB 


SB Pupils 


988 


61 




62 




65 




82 




Sales.- 


98 
17 
39 

7 


53 
49 
58 
65 


—8 

—12 

—3 

+4 


68 
56 
66 
74 


+6 

—6 

+4 

+ 12 


61 
59 
67 
63 


—4 
—6 
+2 
—2 


107 

128 

95 

99 


+25 

+46 
+ 13 
+ 17 


Billers _. 


Checkers 




Eutire outside 


161 


54 


—7 


66 


+4 


63 


—2 


106 


+24 





45 



The data in Table XII are presented in figure 21 in terms of the 
amounts by which each employee group exceeded or fell below the 
8B medians. 



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it it I 4- T ^^ 


: :""'_^ :: xtx x : ._ ixx-xit^'^x.. x 


/ \ -^ 


±_-*i>._: z.^t I :_ J I- x: :_^'±±_: ; 


*'-^ J ^ \ y + 


h --\- V- ^-t •'4-i^---- 




1 / y -^ " 


X ' ~ 'iY .."" ,. _. : X t - -4,^" ' it :.. : 


T 7 ) .'- 


^ _( -^ — ^ ._ J^_^^ _. ^ _j^ - ---- 




_, .. ..i| _ _ ..X -4- -,^ - - _- - 






^ """ " ± ± :: 4:"" ^iti: ^s.-""._: "1::: 




_. _ X z_. ,.. _ _x X ^ _ "■ ± "" ""_"" "^v'": - '.-I 




X 2 X3?XX - i -. ..- --it 


. X t^j.i^ X 1l ' ,'S 




Zi: '" X " 117' ?"•-.. x^ j^v. - -■ - _ - 






±i±Sxx^^4^£[!i±iix^x::i3yxii:ffi 


■<^^ --. ''>' ^ > 


^ --■■:.:. N^ ?' /- X ~ it" ^^ it " 


--it - it ^C 1 --i-Sc ^ - - X ~ it ^ '■■JI 


1 L.,,_ _^ ._ --^ ^ „ ...,_,_ ^'•_ 1 _!_ . _|_J- 




"^ ■• ^ 


■ A "^ •» • ' 


"•"t "t ~~ " it~1rir"'^-' d""-""" — "t ""ii"" ' — t"" 


' / 


1 


j 






> 1 1 


— ^— - — lU ij.„. ■ ! , i !! , 



In form the salespeople fell 8 points below the SB median, the 
billers 12 points, the checkers 3 points. The bookkeepers alone 
exceeded the 8B median, to the extent of 4 points. In movement, 
three of the four groups exceeded the 8B median, the billers falling 
below. In spacing, the outside group on the whole fell slightly below, 
the checkers this time being the only group to exceed the school 
median. 

In speed the employee group greatly exceed the rate of the SB 
pupils, the salespeople writing at the rate of 107 letters per minute 
or 25 letters above the SB median, the billers 12S letters or 36 above, 
the checkers 95 or 13 above and the bookkeepers 99 or 17 letters 
above the SB rate. 



46 



The data presented above while suggestive are not conclusive. 
It is planned to continue the investigation so as to secure more 
accurate and complete data as to the demands for writing skill that 
are presented by the needs of the outside world. 

2. Tentative Standards for Each Grade 

The following table presents the tentative grade standards pro- 
posed for each element. They are shown in figures 22 and 23 in 
comparison with the upper quartiles and city wide medians. 

TABLE XIII— tentative STANDARDS IN PENMANSHIP FOR THE NEW 
YORK PENMANSHIP SCALE 



Grade 


Form 


Movement 


Spacing 


Speed 


4B 


43 
47 
51 
54 
57 
59 
61 
63 
65 


46 
48 
50 
53 
56 
59 
62 
65 
67 


48 
51 
54 
57 
60 
63 
65 
67 
69 


56 


5A.__ 


59 


5B 


63 


6A 


67 


6B 

7A 


71 
75 


7B 


80 


8A. 

8B. __ 


85 
90 







For the 8B standard in form the average of the scores attained 
by the classes which exceeded the city wide grade median was 
taken. This score of 65 is already reached by 35 percent, of the 8B 
group tested or by 10 of the 33 classes involved. The lower end 
of the curve was begun at 43, the city wide median for the 4B. Th'fe 
cur\^e of the grade standards was raised from the median curve, in 
some places arbitrarily, and in other places through smoothing to 
the points indicated In the 6B, 7A, and 7B, the grade medians were 
on a level whereas the "standard" curve maintains an even progress. 

The same procedure was followed in the elements of movement 
and spacing, for which the proposed standards are presented in 
Figures 22 and 23. 

For speed the standards adopted are taken from those set up by 
Freeman. Figure 23 shows that in the lower grades such speed 
norms are below the grade medians. 

The above standards are frankly tentative. When the achieve- 
ments of the better schools are considered, they are not regarded as 
imreasonable nor difficult of accomplishment. The schools are work- 
ing imder a uniform time allotment and what is accomplished in some 
of the schools ought to be attainable elsewhere. 

47 



5|B 6, 




MCM/ EMENT 




ENTATI 
GRADE 
OARDS 



6B lA -m Ms &B_ 




3. The Value of -Grade Standards 
The movement for standard educational measurements has for 
one of its chief purposes the setting up of definite aims in the various 
subjects of the curriculiim. For instance, the penmanship in our 
elementary schools aims to give the pupil a certain degree of writing 
skill. The course of study prescribes that seventy-five minutes a 
week be devoted to penmanship in the lA to 6B grades and in that 
time the child be trained to write with legibility, ease and speed. 
Such aims are vague and indefinite and therefore afford no material 
guidance to the teacher and the principal in their work in penmanship. 



49 



Contrast the aim to teach an 8B pupil ''to write with speed" with the 
aim "to write at the rate of 90 letters a minute." Contrast the aim 
"to write with legibility" with the aim "to write with a letter forma- 
tion or quality equal to step 70 on the New York Scale." The use 
of standards provides definite teaching aims. 

With definite aims set up the efforts of the teacher can be 
directed toward the specific goal instead of being spread over an 
indefinite field. With accurate means of measurement now available 
the teacher can readily find out how near she is coming toward achiev- 
ing her goal and upon what to lay stress in order to attain her aim. 
In short it permits the teacher to plan her work more effectively. 

They afford a basis with which to compare the present accom- 
plishments of the pupils and thus to determine which pupils are below 
standard or above standard. 

They provide definite goals for the pupils also. In this the use of 
standards will prove an effective means of motivating the instruction. 



fllJPFRVISORV 


Ol 


?APH 


Showing 


G 


RAOE 


STANDARDft 






4B 


5A 


5B 6A 


6B 7A 7R RA 


P> 


3 

5 

r 

9 




Form 




1 1 1 


1 1 1 


1 1 


1 1 




1 


1 




4 


3 4 


7 


5 


1 5 


4 


5|7 5l 


9 6 


1 63 


6 


Movement 




1 


1 


1 1 


Mill 


1 


1 1 


1 


4 


6 


^ 


8 5 


5 


3 


sie 5 


9 6 


Z- 6 


5 


6 


Spacing 




1 


1 1 


1 


1 


1 


1 


1 


1 


4 


8 


' 


1 5 


4 5 


7 6 


6 


3 6 


5 67 


6 


Speed 




1 


II 


1 1 1 


1 1 


I 1 1 1 


III 


1 1 1 1 


5 


6 


5 


9 65 6 


7 


7 


1 T 


5 8 


8 


5 


' 






Fig XXIV- 









They provide a basis for making more effective the supervisory 
efforts of the principal and the superintendent. Figure 24 shows a 
graph which may be used for such purpose. The graph shows 
the standards in fonn, movement, spacing and speed for each grade. 
The standards for the 4B, for instance, are 43 in form, 46 in move- 
ment, 48 in spacing and 56 in speed. A 4B class that was standard 
in achievement in all elements would be indicated on the graph by a 
vertical line coinciding with the vertical line under 4B . 

Figure 25 shows the use of this graph in a comparison of the 
achievements of SB pupils in twelve schools. From this diagram it is 
possible to discover the elements in which a class is below standard 
and also the extent to which it is below standard. The graph shows 
that these classes are nearer the 8B standard in speed than they are 
in the other elements. It shows the wide variability in the perform- 
ance of different schools. While some are above standard in form 
most of the twelve schools are below, several in fact showing but sixth 
year achievement. The superintendent is able to diagnose the situ- 
ation in his district with respect to penmanship and to determine 
where his attention should be directed. 

50 





SuPFRvi5;oRY Graph Showima Gqa 


D_E Standards 






4-R 5A SB 6A 6R 7A 7R «A fiR 


Form 




1 1 1 


III II II 


1 


1 


1 


1 


1 


1 


1 


4 


3 4 


'" 5' ^^:y ^ 


7 5 


^ , ' 


S^ ' 


3 « 


5 S 


7 6 


r ^ 


MovEMEWT 




1 




\' 


M^l 1/ 


N- 


-rV 


\l 


1 


1 


^ 


4 


6 4 


8 5 


" A 




6 ~^S 


9 ^ 


^>^ 


^ el7 e 


' ^' 


' ) 


Spacing^ 




1 1 


1 1 


A \ 


Kl 


\/A 


^> 




^1 




/ 


r 


4 8 5 


', ,r 


4 5 


7 ■-< 


tM^ 


^<^ 


5 /6 


l> - ^ 


/ 7 


V ' 


Speed 




1 1 


II 


iiL^^^iir 


^^ 




i^JJ- 


^ 1 


m-r Mil 






9 U 


J-— ^ 67 T 


' ' 


5 ^ 




L5<$«, ^ 


S 10 1 


t Twelve 8B faRAPesJN.DiFFEBENT :Sr.Hooi--, Fic.X.XV 



Figiire 26 shows the achievements of five. 6B classes in the same 
school. Ordinarily it would be reasonable for us to expect that the 
scores of such classes would show agreement more or less close. The 
variability is apparent. In form two classes are below standard, 
two standard and one above. In movement one is below, two are 
quite close to standard and two are above. In spacing all are above. 
In speed there are three above and two below. The existing situa- 
tion is made clear to the principal of this school who may now direct 
his attention more effectively where it is most needed. 
SuPFRVisoRY Graph 5>Hf)wiMfi Graof .ST A NnAgns 




In conclusion attention is called to one of the principles under- 
lying all educational measurements, and that is the principle of the 
limitation of training. This principle means that as soon as a child 
has surpassed the standard of his grade he should be excused from any 
ftirther direct training and should be given more profitable work. 
Particularly should this apply if the pupil has attained the skill set 
up as the ultimate goal of the elementary school. If the needs of the 
outside world have been a factor in determining such standards, as 
they should be, any further development of skill beyond such stand- 
ards will not probably be a factor in determining the social efficiency 
of the individual. The development of higher levels of ability in 
preparation for a specific vocation is not the function of the elementary 
schools. Again, individuals with greater natural capacities will 
reach the standard level with much less training than individuals less 
favored by natiu-al inheritance, and consequently for such individuals 
drill soon comes to have little meaning and in fact may be harmful. 
For the exceptionally able child the incidental training which comes 
through the use of his mechanical skill in real work, once the standard 
has been reached, will automatically develop his ability to higher 
levels without direct drill. The ordinary child, on the other hand, 
may probably require continuous direct drill to maintain his level. 



51 



APPENDICES 



APPENDIX A 
Methods of Scoring Employed in This Survey 

The scoring of the resulting twelve thousand samples of penman- 
ship in each of the elements of form, movement, spacing and speed, 
represented an enormous task. The task was undertaken by Dr. 
Hamilton and Miss Scheuerman of the New York Training School 
for Teachers and by Mr. Lister of the Brooklyn Training School for 
Teachers. The services of training school students were enlisted. 

While it is generally conceded that the use of a penmanship scale 
in the hands of trained scorers reduces considerably the variability 
in judgment which obtains when specimens are scored without such 
aid, it is also true that in the hands of untrained persons the penman- 
ship scale gives no guarantee that the resulting judgments will be 
reliable. Nor does a knowledge of the theories underlying educational 
measurements or the statistical derivation of scales insure acciurate 
scoring. Likewise expertness in teaching penmanship, while of some 
help, is not synonymous with reliability in scoring. To obtain accu- 
racy in scoring there must be training in the use of the scale. 

Investigations by Kelly and others have shown that teachers 
using the percent, method of rating have reduced their variability by 
practice at the expense of the children, while they have at the same 
time decreased their capacity for effective use of a standard scale. 

It was considered advisable for the above and for other reasons 
to employ as scorers training school students rather than the teachers. 
The training school students who acted as judges had the following 
qualifications. — (1) They had been instructed in the muscular move- 
ment method of writing. (2) They had taken the normal course in 
teaching that method. (3) They had also had the course in educa- 
tional measurements in the training school as a result of which they 
were familiar with the various penmanship scales and in the course 
of which they had received some practice in giving standard tests and 
in judging specimens of penmanship by means of standard scales. 

To supplement the above favorable conditions, it was arranged 
to give the students, who were to act as scorers, specific instruction 
and training for a period of three weeks or longer in the use of the 
New York Scale through actual practice in judging specimens.. 

52 



For use in the training of the judges standard specimens 
of writing were prepared, that is, the specimens were scored by 
one of the authors of the scale and four of his associates and a score 
assigned for each of the elements of form, movement and spacing. 
The specimens were coded so that the students were unaware of the 
''expert" score. 

In scoring these practice samples, and subsequently the test 
papers, the ascending-descending method was used. 

It was planned to give the student judges an initial test in 
scoring and at the end of the practice period a final test. The data 
resulting from these tests would afford a measure of the reliability 
of each prospective judge and a basis for eliminating some of the 
students from participation in scoring the test papers. Unfortu- 
nately school conditions and other circumstances prevented us from 
carrying out our programme in its entirety. We were, however, 
able to get an initial test for all the student judges and a final test 
for part of the group. 

Table XIV shows for the initial test the average deviation per 
specimen from "expert" scores for the group of prospectve judges. 
In this preliminary test there were twenty-one samples used. 



TABLE XIV— AVERAGE DEVIATION PER SPECIMEN FROM "EXPERT" SCORES 
FOR 86 PROSPECTIVE JUDGES— PRACTICE SAMPLES 





Deviation in Points 


Aver- 


Element 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


age 


Form 


3 


3 


8 


24 


20 


15 


11 


2 


1 










1 




1 


5-07 


Move- 




































ment- 


2 




2 


4 


18 


22 


19 


12 


5 


3 








1 




1 


6.5 


Spacing . 




1 


8 


22 


36 


12 


8 


1 




1 














5.05 


Total 


5 


4 


18 


50 


74 


49 


38 


15 


6 


4 








2 


.... 


2 


5.5 



It developed upon later analysis of these results that for those 
of the trial specimens which were taken from the scale there was a 
possibility of identifying the specimens through the content, which 
factor may have influenced the variability of the judging. Accord- 
ingly, those trial specimens which had been taken from the scale 
were excluded and the judgments retabulated on the basis of the 
remaining specimens with the following results : 



53 



TABLE XV— AVERAGE DEVIATIONS PER SPECIMEN FOR "EXPERT" SCORES 
FOR 86 PROSPECTIVE JUDGES— PRACTICE SAMPLES— SECOND TABULATION 











AvEBAQB Deviations 














Av- 


Element 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


er- 
age 




1 






4 


8 

3 
11 


16 

8 
24 


12 

3 

20 


25 

14 
18 


14 

15 

1 


2 

15 
5 


1 

17 
2 


1 

3 
2 


3 


1 


1 
1 


1 


1 

2 


7 P 


Move- 
ment 






10 1 


Spacing.. 






1 


2 


7.4 


Total 


1 




1 


6 


22 


48 


35 


57 


30 


22 


20 


6 


3 


1 


2 


1 


3 


8.3 



The above table shows the average deviation of each of the 86 
prospective judges in scoring the practice samples. Under form, for 
instance, one judge deviated on the average from 1 to 2 points from 
the "standard" scores given the practice samples, 4 deviated on the 
average 4 points, 8 deviated 5 points, and so on. The average of 
these average deviations was 7.9 for form, 10.1 for movement and 
7.4 for spacing. The greatest deviation appeared in the element of 
movement. 



TABLE XVI— DEVIATIONS PER JUDGMENT 



Element 


^0 


35 


30 


25 


20 


15 


10 


5 





+5 


10 


15 


20 


25 


30 


35 


40 


Total 


Aver. 


Form .. 




2 
22 

1 


11 

20 

2 


12 

38 

4 


26 
89 
16 


46 
51 
76 


134 
211 

97 


134 
168 
226 


300 
171 
216 


154 
206 
317 


156 

28 
118 


78 
85 
86 


35 

5 

17 


12 
20 
16 


12 
2 
3 


1 

4 
2 


1 
1 


1,114 
1,125 
1,199 


7 9 


Movement.... 
Spacing. 


5 

1 


10.1 
7.2 


Total 


6 


25 


33 


54 


131 


173 


442 


528 


687 


677 


302 


249 


57 


48 


17 


7 


2 


3,438 


8.4 



Table XVI shows the distribution of the judgments given by the 
86 prospective judges in scoring the practice samples, in terms of their 
deviations plus and minus from the standard or expert scores. The 
table is read as follows : 

Out of 1,114 judgments in form given by the 86 judges 2 were 35 
points below the "expert" score, 11 fell 30 points below, 12, 25 points 
below, and so on. Three hundred judgments agreed with the "expert" 
score, 154 exceeded it by 5 points, 156 by 10 points and so on. Like- 
wise for the other elements. 

Table XVII shows for each element the nimiber and percent, of 
judgments that deviated by various scale amounts. 



54 



TABLE XVII— DEVIATION ACCORDING TO AMOUNT 



Deviations 


FOHM 


Movement 


Spacing 


Total 


No. 


Percent. 


No. 


Percent. 


No. 


Percent. 


No. 


Percent. 


Zero deviations — 

5 points or \^ step 
10 points or 1 step.. 
15 points or ij^ step 
20 or 2 steps or more 


300 
288 
290 
124 
112 


26.9 
25,9 
26.0 
11.1 
10.0 


171 
374 
239 
136 
205 


15.2 
33.2 
21.2 
12.1 

18.2 


216 
643 
215 
162 
63 


18.0 
45.3 
18.0 
13.5 
6.2 


687 
1,205 
744 
422 
380 


20.0 
35.1 
21.6 
12.3 
11.0 


Total 


1,114 


99.9 


1,125 


99.9 


1,199 


100.0 


3,438 


100.0 



Under form it v^ill be seen that 878 or 78.8 percent, of the judg- 
ments fell within one step of the scale from the "standard or expert" 
score. In movement 69.6 percent, of the judgments deviated one 
step or less, while in spacing the number of such judgments was 81.3 
percent. 

It is to be borne in mind that the above data are for the initial 
test given at the beginning of the period during which it was planned 
to give rather intensive training to those students who were to serve 
as scorers. While school conditions and extraneous circumstances 
prevented us from carrying out our programme in its entirety, it is 
believed that the variability of those who finally acted as judges was 
considerably reduced from the degree indicated in the above table. 

For a number of the judges to whom a second formal test was 
given it was possible to secure data which indicated the improvement 
attained. Table XVIII shows for 56 of our prospective judges the 
average deviations in the initial test in comparison with the results 
of the final test. 

From this table it is seen that the average deviation for the 56 
judges on the initial test was 7.5 points on the scale or ^ of a step. 
On the second test, several weeks later, the average deviation of the 
group was 4.2 points or less than 3^ of a scale step. The figures to 
the left of the heavy zigzag line indicate the students who showed 
improvement in scoring. Those to the right of the line represent 
the students whose scoring showed the same amount of deviation or 
an increase therein. For instance, there were 17 students whose 
average deviation on the first test was 8 points. On the second 
test these 17 students were distributed as follows: 1 deviated less 
than one point; 1 deviated one point; 5 deviated two points; 2, 
six points; and 1, seven points. All these showed considerable 
improvement. On the other hand, 4 deviated nine points or one 
point more on the second test than on the first test; 1, ten points 
and 1, eleven points. These six showed a loss in accuracy. Of the 



55 



56 students, 42 showed improvement, in some cases marked, 3 showed 
no progress, while 11 showed a sHght loss, that is an increase in varia- 
bility. 

TABLE XVIII— AVERAGE DEVIATIONS FOR 56 PROSPECTIVE JUDGES IN 

TWO TESTS 





Average Deviations — 2d Test 


Total 


Devia- 
tions 


0-1 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


n 


12 


13 


14 


15 


16 


17 


18 


1st 
Test 


18 






































1 


1 


17 


















1 


















1 


16 






































15 








































14 










































13 








































12 










1 




























1 


11 












1 






















1 


10 










1 

1 
1 


2 

1 


2 
2 

[l 


2 

1 


4 
1 


















1 


9 


2 

1 
1 
2 
2 


1 
1 


5 

3 

1 
1 


1 

1 

3 

1 

.1 


1 
1 


















8 


8 


1 
















17 


7 
















6 


6 ...._ 




















11 


5 
























6 


4 






























2 


3 






































2 








































1 . 




1 




































1 










































Totals 
2nd Test.... 


8 


3 


10 


7 


4 


4 


5 


2 


4 


5 


2 


1 














1 


56 




















Average 4.5 


Aver. 
7.5 



.^l) 



APPENDIX B 

Reliability of the Scoring 

The papers of about 15 percent, of the classes involved in the 
test were scored by groups of three judges, each scorer working 
independently. The data from twenty such classes were ana- 
lyzed and afford a fair measure of the reliability of the scoring 
in general. 

Table XIX shows as an illustration the scores in form assigned 
by three judges to each paper in a 5 A class. The table is to be read 
as follows: — ^Judge I rated the paper of pupil number 1, at 30 on the 
scale in form, Judge II rated it as worth 25, and Judge III assigned 
the mark of 30. The median of the three judgments was 30. The 
• scores of Judge I and III showed zero deviation, while that of Judge 

II was 5 points below. The total deviation of the group from the 
median score was 5 points, or an average of 1.7 points. Out of the 
total of forty specimens in the class, the three judges agreed absolutely 
as to the value of 13, or about one-third of the papers. On most of 
the other samples also the judges showed very close agreement. In 
only a few cases is there any wide variation, for instance, papers 
No. 7 and 18. 

At the bottom of the columns headed "Deviations" appears the 
simi of the deviations of the scores of each judge. Judge I shows a 
total of 70 on the 40 papers, or an average deviation of 1.8 points; 
Judge II has a total of 130 or an average deviation of 3.3 points, while 
Judge III deviated on the average only four tenths of a point. The 
total deviation on the entire set of papers for the three scorers 
was 215 or an average of 1.8 points, less than a fifth of a step 
on the scale. 

At the foot of the columns headed ''scores" appears the medians 
based upon the scores given by each judge. The median of the 
scores given by Judge I is computed at 39.5, that of Judge II at40.7, 
and that of Judge III at 39.4. The median class score computed 
from the median score on each sample is 40. The class medians given 
by the three judges are practically identical, Judge I differing but 
by five tenths of a point, Judge II by only seven tenths and Judge 

III by six tenths of a point. The average deviation of class medians 
for the three judges from the class median computed from the median 
score on each sample is but six tenths of a point. 

57 



TABLE XIX— SCORES IN FORM OF A FIFTH GRADE CLASS GIVEN BY 
THREE JUDGES SCORING INDEPENDENTLY 



Pupil's 


scohb accobding to 
Judge 


Median 
Score 


Deviation op 
Judge 


Each 


Total 


Average 


Sample 


I 


II 


III 


I 


II 


III 


Dev. 


1 


30 
30 
35 
40 
40 
40 
45 
35 
35 
25 
35 
50 
40 
40 
30 
35 
30 
30 
40 
40 
30 
40 
35 
35 
30 
40 
30 
40 
45 
45 
40 
30 
40 
40 
25 
40 
35 
35 
40 
35 


25 
35 
40 
40 
40 
45 
70 
35 
25 
25 
25 
60 
35 
35 
25 
25 
25 
45 
35 
50 
40 
50 
25 
40 
25 
45 
30 
40 
45 
40 
40 
40 
40 
40 
25 
40 
35 
35 
40 
40 


30 
35 
35 
40 
40 
35 
50 
35 
25 
25 
35 
60 
40 
40 
25 
35 
25 
30 
35 
40 
30 
40 
30 
40 
30 
45 
30 
40 
45 
45 
40 
40 
40 
. 45 
25 
40 
35 
30 
40 
35 


30 
35 
35 
40 
40 
40 
50 
35 
25 
25 
35 
60 
40 
40 
25 
35 
25 
30 
35 
40 
30 
40 
30 
40 
30 
45 
30 
40 
45 
45 
40 
40 
40 
40 
25 
40 
35 
35 
40 
35 




—5 





—5 

+10 


—10 



+5 


+5 


+5 




+5 

—5 


—5 





—10 










—5 


+5 



+5 
+20 



—10 


—5 

—5 



—10 



+15 



+ 10 

+10 

+10 

—5 


—5 





— 5 










+5 








—5 










0. 

















+5 




—5 




5 

5 

5 





10 

25 



10 



10 

10 

5 

5 

5 

10 

5 

15 

5 

10 

10 

10 

10 

5 

5 

5 







5 



10 



5 







5 



5 


1.7 


2 

3.. 


1.7 
1.7 


4 


0.0 


5 


0.0 


6 

7... 


3.3 

8.3 


8 


0.0 


9 


3.3 


10 


0.0 


11 


3.3 


12.. 


3.3 


13. 


1.7 


14. 


1.7 


15.. 


1.7 


16 


3.3 


17 


1.7 


18 


5.0 


19 


1.7 


20. 


3.3 


21 


3.3 


22.. . 


3.3 


23.. 


3.3 


24.. 


1.7 


25.. 


1.7 


26. 


1.7 


27 

28 


0.0 
0.0 


29... 


0.0 


30.. 


1.7 


31 .. .. 


0.0 


32.. 


3.3 


33.. 


0.0 


34.. 


1.7 


35.. 


0.0 


36. 


0.0 


37-. 


0.0 


38 


1.7 


39 


0.0 


40..-.. 


1.7 






Class 
median 


39.5 


40.7 


39.4 


40 












Totals 










70 


130 


15 


215 




Average 










1.8 


3.3 


0.38 


1.8 





This is remarkably close scoring. It is probably the best per- 
formance revealed by the analysis of the data. The following tables 
will show that while not as excellent a showing was made by the 
other scorers, the scoring was on the whole very consistent and 



quite satisfactory. 



58 



Figure XXVII 

























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The twenty classes for which the data were worked up in detail 
totaled 753 specimens. Each of these specimens received three 
scorings or judgments, making a total of 2,259 judgments. The fol- 



59 



lowing table and figures show the distribution of these judgments in 
terms of deviations from the median score for each paper. 



TABLE XX— DISTRIBUTION OF INDIVIDUAL SCORES IN TERMS OF DEVIA- 
TIONS FROM MEDIAN SCORES ON EACH SAMPLE 





Deviations 


Total 






—30 


—25 


—20 


—15 


—10 


—5 





+ 5 


+10 


+15 


+20 


+25 


+30 




age 


Form 


1 

1 
2 


2 
5 

4 


11 
12 
16 


37 
55 
64 


128 
137 
143 


297 

281 
249 


1,310 
1,249 

1,279 


278 
300 
288 


131 
152 
140 


49 
42 
56 


10 
18 

12 


2 
6 
6 


3 

1 


2,2.59 
2,259 
2,259 


3 27 


Movement.— 
Spacing— 


3..62 
3..62 


Total- 


4 


11 


39 


156 


408 


827 


3,838 


866 


423 


147 


40 


14 


4 


6,777 


3..5 




Form 


Movement 


Spacing 




Number 


Percent. 


Number 


Percent. 


Number 


Percent. 







1,310 
575 
259 
115 


58..0 

25..4 

11..5 

5..1 


1,249 
581 

2S9 
140 


55..3 

25..7 

12..8 

6.-2 


1,279 
537 
283 
160 


56..6 






23-.8 


10 points or 1 step 
More than 10 poin 






12 5 


s or 1 step..-,. 


7..1 


Total 


2.259 


100..0 


2.259 


100..0 


2.259 


100-0 








1 























Out of the total of 2,259 judgments in form, 1,310 or 58.0 per- 
cent, agreed with the median scorej 473 or 20.9 percent, were posi- 
tive deviations and 476 or 21.0 percent, were negative. The lower 
part of the table shows that 25.4 percent, of the judgments deviated 
5 points or one half step on the scale; 11.5 percent, deviated one 
step and 5.1 percent, more than one step. 

In movement 55.3 percent, of the judgments agreed with the 
median scores, 519 or 23.0 percent, were positive deviations, while 
491 or 21.7 percent, were negative. 

Out of the total, 25.7 percent, of the judgments deviated one 
half step on the scale, 12.8 percent, deviated a full step and 6.2 per- 
cent, more than a full step. 

In spacing, 1,279 out of the 2,259 judgments or 56.6 percent, 
agreed with the median scores, 502 or 22.2 percent, were positive 
deviations while 478 or 21.2 percent, were negative. Of the total 
judgments, 23.8 percent, deviated 5 points or half a scale step, 12.5 
percent, deviated a full step and 7.1 percent, more than a scale 
step. 

The average deviation per judgment is 3.3 points in form, 3.6 in 
movement and 3.6 in spacing. This means that on the average 

60 



a judgment by one judge on an individual sample will vary less than 
four tenths of a scale step from the median of three independent 
judgments. 

Looking at the matter from the standpoint of the individual 
judge rather than the individual paper, we may consider the data 
presented in Table XXI. Table XXI shows for each of the sixty 
judges involved the average deviation per sample. These aver- 
age deviations are based on the judgments given to the papers of 
a class compafed with the median score of the group of three judges 
in each case. 

TABLE XXI— AVERAGE DEVIATION PER SAMPLE FOR 60 JUDGES 



Amount 

0.0 to 1 point 

1 to 2 points -. 

2 to 3 points 

3 to 4 points 

4 to 5 points.- 

5 to 6 points.- 

6 to 7 points 

7 to S points 

8 to 9 points. 

9 to 10 points 

Total. 

Average _ 



Form 



Movement 



Spacing 



17 

16 

11 

2 

3 



60 
3.3 



1 

7 

13 

19 

11 

4 

2 

1 

1 



60 
3.6 



17 
10 
9 
6 
1 
3 
1 



60 
3.7 



For instance, two out of the sixty judges showed an average 
deviation on the papers of the classes scored by them of less than 
one point; eight judges differed less than two points; seventeen 
judges deviated on the average less than three points, and so on. 

In form the average of the average deviations for the group of 
sixty judges was 3.3 points per judge, in movement it was 3.6 points, 
and in spacing 3.7 points. 

While the scoring on the whole showed very satisfactory agree- 
ment, there was considerable variation shown by individual judges 
in the case of individual samples. The bulk of the papers were 
scored by a single judge. In order to get a true index of the value of 
any individual paper it would probably be necessary to have such 
paper scored by more than one judge or more than once by the same 
judge. With an increase in the number of judges we would obtain a 
consensus of opinion which would yield us the real value of the paper. 
Otu study, however, was directed more to the performance or achieve- 
ments of groups of pupils rather than of individuals. 

In dealing with the class scores it is probably safe to say that 
such scores are more reliable than any score given to an individual 



61 



paper. On the whole, while the scores of an individual judge may 
vary more or less widely from the median of the three independent 
judgments, the median score for a class set of papers given by one 
judge shows less variation and closer agreement with the class median 
based on the group scores. It is possible and probable that the devi- 
tions of the individual scores for the one judge may counteract each 
other, 

Figure 28 shows graphically the data presented in Table XX, the 
distribution of the 2,259 judgments in terms of their plus or minus 
deviations. In each of the elements the S3nimietrical character of 
the diagrams is to be noted. The number of the positive deviations 
equals or nearly equals the number of negative deviations. In the 
scoring of large groups of papers, the deviations in one direction 
would in all probability be corrected or counteracted by the devia- 
tions in the other directions so that the median as fotmd would 
approximate very closely the actual median value of the group 
performance. 



62 



Fi^yXVlll nrVIATICM?, FRUuMFniAMS-^ISSjlll 



-^(1 -;5 -Pn -l.-i -in -■■; D i.5 llfl >I5 »gll ->25 



63 



TABLE XXII— AVERAGE DEVIATION PER CLASS SCORE FOR TWENTY 
GROUPS OF SCORERS 



Amount 

0.0 to 1.0 point 

1 to 2 points 

2 to 3 points 

3 to 4 points._ 

4 to 5 points.- 

5 to 6 points 

Total 

Average 



Form 



Movement 



Spacing 



20 
2.0 



20 

2.4 



20 

2.S 



Table XXII shows the average deviation of each group of three 
judges from the class median based on the group scores. In form 
out of the 20 groups, 5 groups deviated on the average loss than 1 
point, 7 less than 2 points, 3 less than three and 1 more than four 
points. The average of the average deviations was 2 points in form, 
2.4 points in movement and 2.8 points in spacing. For the individual 
judges rather than for groups, the average of the average deviation in 
form was 2.2 points, in movement 2.6 points and in spacing 2.7 
points. 

On the whole, then, the class medians resulting from the scoring 
of one judge may be taken as the actual value of the writing of the 
class and will be in error less than three points, or three tenths of a 
scale step. 

Our main interest lies not even in the performance of class groups 
but in the achievement of larger grade groups. With the increase in 
numbers involved there is a strong probability that the grade medians 
given for the entire group, involving in each case about 1,000 pupils, 
represents the actual value of the performance of the group. 



64 



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